2015/05/26 by Andrew W. Macpherson, Macpherson, Andrew W.
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG
paper · pdf · doi:10.48550/arxiv.1505.07022
79 pages
openalex publication_date 2015/05/26 · arxiv created 2015/05/28 · arxiv updated 2015/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
I extend the definitions of schemes relative to monoids with zero - and therefore, toric geometry - to the world of formal schemes. This expands the usual framework to include, for instance, models for Mumford's degenerating Abelian varieties. Following the usual toric paradigm, normal formal monoid schemes can be classified in terms of certain cone complexes, and their properties understood in combinatorial terms. I use this to give a simple algebraisation criterion. I also reformulate the traditional notions of separated and proper morphism in a manner amenable to the context of relative formal geometry, and give characterisations in terms of the topology of cone complexes.